Nonstandard Analysis for the Working Mathematician

Description

This book is addressed to mathematicians working in analysis and its applications. The aim is to provide an understandable introduction to the basic theory of non-standard analysis and to illuminate some of its most striking applications.

The presentation is intended to facilitate the acquisition of basic skills in the subject, so that a reader who begins with no background in mathematical logic should find it relatively easy to continue. The particular applications discussed here are in functional analysis including operator theory, probability theory including stochastic processes, and economics including game theory and financial mathematics. In working through this book the reader should gain many new and helpful insights into the enterprise of mathematics. Problems are posed in all chapters.

Table of Contents:
1. A simple introduction to nonstandard analysis;
2. An introduction to general nonstandard analysis;
3. Topology and measure theory.
4. Functional analysis.
5. Measure theory and integration
6. Probability theory
7. Conventional operations on nonstandard constructions.
8. Nonstandard analysis in mathematical economics.

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